zgelss(3F)

NAME
     ZGELSS - compute the minimum norm solution to a complex linear least
     squares problem

SYNOPSIS
     SUBROUTINE ZGELSS( M, N, NRHS, A, LDA, B, LDB, S, RCOND, RANK, WORK,
                        LWORK, RWORK, INFO )

         INTEGER        INFO, LDA, LDB, LWORK, M, N, NRHS, RANK

         DOUBLE         PRECISION RCOND

         DOUBLE         PRECISION RWORK( * ), S( * )

         COMPLEX*16     A( LDA, * ), B( LDB, * ), WORK( * )

PURPOSE
     ZGELSS computes the minimum norm solution to a complex linear least
     squares problem:

     Minimize 2-norm(| b - A*x |).

     using the singular value decomposition (SVD) of A. A is an M-by-N matrix
     which may be rank-deficient.

     Several right hand side vectors b and solution vectors x can be handled
     in a single call; they are stored as the columns of the M-by-NRHS right
     hand side matrix B and the N-by-NRHS solution matrix X.

     The effective rank of A is determined by treating as zero those singular
     values which are less than RCOND times the largest singular value.


ARGUMENTS
     M       (input) INTEGER
             The number of rows of the matrix A. M >= 0.

     N       (input) INTEGER
             The number of columns of the matrix A. N >= 0.

     NRHS    (input) INTEGER
             The number of right hand sides, i.e., the number of columns of
             the matrices B and X. NRHS >= 0.

     A       (input/output) COMPLEX*16 array, dimension (LDA,N)
             On entry, the M-by-N matrix A.  On exit, the first min(m,n) rows
             of A are overwritten with its right singular vectors, stored
             rowwise.

     LDA     (input) INTEGER
             The leading dimension of the array A. LDA >= max(1,M).
     B       (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
             On entry, the M-by-NRHS right hand side matrix B.  On exit, B is
             overwritten by the N-by-NRHS solution matrix X.  If m >= n and
             RANK = n, the residual sum-of-squares for the solution in the i-
             th column is given by the sum of squares of elements n+1:m in
             that column.

     LDB     (input) INTEGER
             The leading dimension of the array B.  LDB >= max(1,M,N).

     S       (output) DOUBLE PRECISION array, dimension (min(M,N))
             The singular values of A in decreasing order.  The condition
             number of A in the 2-norm = S(1)/S(min(m,n)).

     RCOND   (input) DOUBLE PRECISION
             RCOND is used to determine the effective rank of A.  Singular
             values S(i) <= RCOND*S(1) are treated as zero.  If RCOND < 0,
             machine precision is used instead.

     RANK    (output) INTEGER
             The effective rank of A, i.e., the number of singular values
             which are greater than RCOND*S(1).

     WORK    (workspace/output) COMPLEX*16 array, dimension (LWORK)
             On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

     LWORK   (input) INTEGER
             The dimension of the array WORK. LWORK >= 1, and also:  LWORK >=
             2*min(M,N) + max(M,N,NRHS) For good performance, LWORK should
             generally be larger.

     RWORK   (workspace) DOUBLE PRECISION array, dimension (5*min(M,N)-1)

     INFO    (output) INTEGER
             = 0:  successful exit
             < 0:  if INFO = -i, the i-th argument had an illegal value.
             > 0:  the algorithm for computing the SVD failed to converge; if
             INFO = i, i off-diagonal elements of an intermediate bidiagonal
             form did not converge to zero.